examday

/TMUA

The following shape has two lines of reflectional symmetry.

$MNOP$ is a square of perimeter $40\,\text{cm}$.

The vertices of rectangle $RSTU$ lie on the edge of square $MNOP$.

$MR$ has length $x\,\text{cm}$.

What is the largest possible value of $x$ such that $RSTU$ has area $20\,\text{cm}^2$?